$e^{-}$ — Learning: Appliance Level Load Monitoring
In [1]:
from IPython.display import Image
from IPython.core.display import HTML
sns.set_style('whitegrid', {'axes.grid' : False})
%config InlineBackend.figure_format = 'retina'
%matplotlib inline
In [6]:
Image(filename = "images/NILM.jpg", width=500, height=500)
Out[6]:
Goal: Provide estimates of power demand of appliance n at time t
SMART METER¶
In [6]:
Image(filename = "images/smart_meter.jpg", width=400, height=400)
Out[6]:
Tracks and records customer's home electricity use and transmits it back to electric companies
Pojected 90M AMI (2020), USA¶
In [12]:
Image(filename = "images/ami.jpg", width=400, height=400, retina=True)
Out[12]:
Existing ( As of 2015 )
- PG&E : > 5 M
- SCE : > 5 M
- FP&L : 5 M
- Texas Oncor: 3.4 M
Plans
- Chicago Commonwealth Edison (1.8M out of 4.3M planned)
- Con Edison (3.6M by 2021)
WHAT YOU DO SEE:¶
In [7]:
Image(filename = "images/bill.jpg", width=300, height=300, retina=True)
Out[7]:
WHAT YOU DON'T SEE:¶
In [8]:
Image(filename = "images/appliances.png", width=500, height=600, retina=True)
Out[8]:
WHY is this Important?¶
- Growth in energy consumption
- Enable automated energy management systems
- Opportunity to reduce waste!
EXAMPLE¶
In [91]:
table = FF.create_table(example)
py.iplot(table, filename='sample_costs')
Out[91]:
The underlying assumption in the first cost column is that the applaince is on for 5 hrs/day for a month, while being on for 24 hrs/day in the second cost column. The difference column shows the financial impact of these two cases of appliance usage. For the 5 seemingly low level appliances, a customer can expect a bill differing up to \$40/month
In [23]:
Image(filename = "images/process.png", width=500, height=600, retina=False)
Out[23]:
``` | Datasets | Institution | Location | |-----------------|-----------------|--------------| | REDD (2011) | MIT | MA, USA | | BLUED (2012) | CMU | PA, USA | | Smart* (2012) | UMass | MA, USA | | Tracebase (2012)| Darmstadt | Germany | | Sample (2013) | Pecan Street | TX, USA | | HES (2013) | DECC, DEFRA | UK | | AMPds (2013) | Simon Fraser U. | BC, Canada | | iAWE (2013) | IIT Delhi | Delhi, India | | UK-DALE (2014) | Imperial College| London, UK | | DREDD (2015) | TUDelft | Netherlands | ```
APPLIANCE DATA¶
In [26]:
Image(filename = "images/data.png", width=500, height=600, retina=False)
Out[26]:
EXPLORING THE APPLIANCE SIGNALS¶
In [11]:
data.head()
Out[11]:
In [16]:
print "%-25s | %-10s | %-10s | %-10s | %-10s | %-10s\n" %('Applaince', 'Min', 'Mean', 'Mode', 'Median', 'Max')
for j in data.columns:
app_data = data[j]
print "%-25s | %-10s | %-10s | %-10s | %-10s | %-10s" \
%(j, app_data.min(), round(app_data.mean(), 2), Counter(app_data).most_common(1)[0][0] ,
round(np.median(app_data.unique())), app_data.max())
In [13]:
fig, ax = plt.subplots(3,3, figsize=(14, 7))
bin_num = 25
color='b'
ax[0,0].hist(data.fridge, bins=bin_num, label='Fridge', color=color)
ax[0,1].hist(data.electric_heating_element, bins=bin_num, label='Elec_Heater', color=color)
ax[0,2].hist(data.cooker, bins=bin_num, label='Cooker', color=color)
ax[1,0].hist(data.sockets, bins=bin_num, label='Sockets', color=color)
ax[1,1].hist(data.toaster, bins=bin_num, label='Toaster', color=color)
ax[1,2].hist(data.laptop_computer, bins=bin_num, label='Laptop', color=color)
ax[2,0].hist(data.washing_machine, bins=bin_num, label='Washing Machine', color=color)
ax[2,1].hist(data.fan, bins=bin_num, label='Fan', color=color)
ax[2,2].hist(data.television, bins=bin_num, label='Television', color=color)
for row in range(3):
for col in range(3):
ax[row,col].set_yticklabels([])
ax[row,col].legend()
ax[0,1].set_title('Appliance Power Distributions\n', fontsize=15)
ax[1,0].set_ylabel('frequency', fontsize=14)
ax[2,1].set_xlabel('Power (Watts)', fontsize=14)
plt.show()
APPLIANCE TYPES¶
- Type I: Single State [ON/OFF]
- Table Lamp
- Type II: Multi-State
- Finite State Machines (FSM)
- Washing Machine
- Type III: Continuously Varying State
- Continuously Variable Devices (CVD)
- Dimmer Lights
- Type IV: Remain active at constant rate
- Smoke Detector, Cable TV Receivers
In [24]:
for appliance in model:
plt.figure(figsize=(9,3))
plt.plot(power[appliance][:86400], color='b')
plt.title("Sample %s Power" %(appliance))
plt.xlabel("index")
plt.ylabel("Power (W)");
Factorial Hidden Markov Model¶
HMM is a mixture model encoding information about the history of a time series in the value of a single multinomial variable — the hidden state — which can take on K discrete values
In [28]:
Image(filename = "images/fhmm.png", width=400, height=400, retina=False)
Out[28]:
Given $\Theta${$\pi$, A, $\Phi$} & X Find optimal Z
Given $\Theta${$\pi$, A, $\Phi$} & X Find P(X|$\Theta$,X)
Given X Estimate $\Theta${$\pi$, A, $\Phi$}
STEPS¶
- Estimate $\Theta$ for each appliance given the data
- Decode hidden states per appliance using estimated $\Theta$
- Combine HMMs to create FHMM
- Decode aggregated signal using FHMM to get hidden state per appliance
- Compare hidden states and power draw
Assumptions¶
Limited Horizon: $P(Z_{t}\ |\ Z_{t-1}, Z_{t-2},..., Z_{1}) = P(Z_{t}\ |\ Z_{t-1})$
Stationary Process: $P(Z_{t}\ |\ Z_{t-1}) = P(Z_{2}\ |\ Z_{1});\ t\ \in\ 2,...,T$
In [80]:
import plotly.plotly as py
import plotly.graph_objs as go
main = go.Scatter(x=simulation.index, y=simulation.Total, name ="Aggregate", line=dict(color='#0d2be8'), opacity=0.8)
app_1 = go.Scatter(x=simulation.index, y=simulation.Fridge, name ="Fridge", line=dict(color='#7F7F7F'), opacity=0.8)
app_2 = go.Scatter(x=simulation.index, y=simulation['Washing-Machine'], name ="Washing-Machine", line=dict(color='#46846e'), opacity=0.8)
app_3 = go.Scatter(x=simulation.index, y=simulation['E-Heater'], name="E-Heater", line=dict(color='#17BECF'), opacity=0.8)
app_4 = go.Scatter(x=simulation.index, y=simulation.Laptop, name="Laptop", line=dict(color='#2a465e'), opacity=0.8)
data = [main, app_1, app_2, app_3, app_4]
layout = dict(title = "Appliance Disaggregation")
fig = dict(data=data, layout=layout)
py.iplot(fig)
Out[80]:
In [10]:
Image(filename = "images/hmms.png", width=600, height=600, retina=False)
Out[10]:
WEAKNESSES¶
- Complexity: O(TK$^N$)
- Adding a new appliance requires retraining the whole model
- Inability to distinguish between applainces with overlapping power changes
METRICS FOR EVALUATION¶
$$Total\ Energy\ Error = \left|\sum_{t}y_t^{(n)}- \sum_{t}\hat{y}_t^{(n)}\right|$$$$ $$$$Normalized\ Error = \frac{\sum_{t}\left|y_t^{(n)}- \hat{y}_t^{(n)}\right|}{\sum_{t}y_t^{(n)}}$$$$ $$$$RMS = \sqrt{\frac{1}{T}\sum_{t}(y_t^{(n)}- \hat{y}_t^{(n)})}$$$$ $$$$Precision = \frac{TP}{TP + FP}$$$$ $$$$Recall = \frac{TP}{TP + FN}$$$$ $$$$F_{1}\ Score = \frac{2 * PRE * REC}{PRE + REC}$$SAMPLE RESULTS¶
``` | Appliance | Baseline Precision | |-----------------|---------------------| | Electric Heater | OFF: 0.72 ON: 0.28 | | Refridgerator | OFF: 0.68 ON: 0.32 | | Laptop | OFF: 0.81 ON: 0.19 | | Washing Machine | OFF: 0.99 ON: 0.01 | ```
``` | Appliance | Precision | Recall | F1-Score | |-----------------|---------------------|---------------------|---------------------| | Electric Heater | OFF: 0.89 ON: 0.82 | OFF: 0.94 ON: 0.71 | OFF: 0.91 ON: 0.76 | | Refridgerator | OFF: 0.94 ON: 0.89 | OFF: 0.95 ON: 0.88 | OFF: 0.95 ON: 0.89 | | Laptop | OFF: 0.89 ON: 0.38 | OFF: 0.76 ON: 0.61 | OFF: 0.82 ON: 0.47 | | Washing Machine | OFF: 1.00 ON: 0.14 | OFF: 0.97 ON: 0.50 | OFF: 0.98 ON: 0.22 | ```
In [35]:
# COMPARING TRUE VS REAL POWER DIST IN TEST SET
for appliance in model:
fig, ax = plt.subplots(1,3, figsize=(14,3), sharey=True)
ax[0].plot(power_test[appliance][:8000], color='b', label='True')
ax[0].set_title('Ground Truth Power for %s' %appliance)
ax[0].legend()
ax[1].plot(decoded_power_test[appliance][:8000], color='g', label='Predicted')
ax[1].set_title('FHMM Predicted Power for %s' %appliance)
ax[1].legend()
ax[2].plot(power_test[appliance][:8000], color='b', label='True')
ax[2].plot(decoded_power_test[appliance][:8000], color='g', label='Predicted')
ax[2].set_title('True vs. Predicted (%s)' %appliance)
ax[2].legend()
plt.ylim((np.min(power_test[appliance])-10, np.max(power_test[appliance])+10))
plt.tight_layout()
In [79]:
import plotly.plotly as py
import plotly.graph_objs as go
main = go.Scatter(x=simulation_test.index, y=simulation_test.Total, name="Aggregate", line=dict(color='#0d2be8'), opacity=0.8)
app_1 = go.Scatter(x=simulation_test.index, y=simulation_test.Fridge, name = "Fridge",
line = dict(color = '#7F7F7F'), opacity = 0.8)
app_2 = go.Scatter(x=simulation_test.index, y=simulation_test['Washing-Machine'], name = "Washing-Machine",
line = dict(color = '#46846e'), opacity = 0.8)
app_3 = go.Scatter(x=simulation_test.index, y=simulation_test['E-Heater'], name = "E-Heater",
line = dict(color = '#17BECF'), opacity = 0.8)
app_4 = go.Scatter(x=simulation_test.index, y=simulation_test.Laptop, name = "Laptop",
line = dict(color = '#2a465e'), opacity = 0.8)
data_test = [main, app_1, app_2, app_3, app_4]
layout = dict(title = "Predicted Disaggregation")
fig = dict(data=data_test, layout=layout)
py.iplot(fig)
Out[79]:
``` | Appliance | RMS Baseline | RMS Model | |-----------------|-----------------|----------------| | Electric Heater | 30 W | 21 W | | Refridgerator | 44 W | 25 W | | Laptop | 11 W | 12 W | | Washing Machine | 58 W | 59 W | ```
Conclusion¶
Non-Intrusive Load Monitoring (NILM) has the potential to create additional value out of already existing metersets. The estimates at each time slice vary in terms of "closeness" for each appliance, which may suggest that the most immediate solution is to inform consumers on the usage of certain appliances. However, you lose out on reducing waste from the "unusual suspect" class of appliances.
``` |Consumer Value | Business Value | |---------------|-------------------| | Transparency | DSM | | Control | Energy Efficiency | | Save Money!!! | Dynamic Pricing | ```
Next Steps¶
- Continue modeling and cross validations, as this is key to generalizing across metersets
- Research community growing: International Workshop on Non-Intrusive Load Monitoring.
- General Electrics's Internet of Energy vision